Hi.
It's hard to know what might change your mom's mind without knowing what influenced her decision to place you in a boarding school, but addressing her core reasons for doing so might help you to convince her to allow you to come home.
Were you enrolled because your grades were falling in a public school? If so, you might want to suggest ways you can get academic support in your hometown or ask your mom to help you research this.
Were you sent to a boarding school because of disciplinary problems? If so, then make sincere amends and let her know that you understand the issue now and will try to correct it--if that is, indeed, the case.
If it is because of conflict within the family, then get an ally such as the school counselor or an independent counselor to help you and your family sort through the issue.
Also, a counselor at the school where you attend may be able to speak with your mother to let her know how much you are suffering, especially if the situation is interfering with your ability to concentrate on your school work or affecting your mental state, which it sounds as though it is. The counselor may be able to talk with your mom about this. Sometimes hearing something from an adult "authority" helps.
Another thought is this: If you are newly enrolled, you may want to allow some time to get accustomed to the place. Then see if you truly hate being there and still want to go home.
Take care.
